Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#418 | C2 | semidirect |
| 3. C2×#88073 | C2 | semidirect |
| 4. C2×#88063 | C2 | semidirect |
| 5. C2×#88062 | C2 | semidirect |
| 6. #11718662 | C2 | semidirect |
| 7. #11718658 | C2 | semidirect |
| 15. C2×#6104 | C4 | semidirect |
| 92. #418 | D13 | semidirect |
| 170. C13 | #1978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6104 | 2 |
| C13×#418 | 2 |
| C2×#88073 | 2 |
| C2×#88063 | 2 |
| C2×#88062 | 2 |
| #11718662 | 2 |
| #11718658 | 2 |
| #1978 | 13 |